1. Direct, Bending, Torsion stresses and Principal Stresses
Dr.R.Ramesh
Professor
Department of Mechanical Engineering
Sri Venkateswara College of Engineering,
Sriperumbudur, chennai

2. TYPE OF LOADS AND STRESSES IN REAL- TIME APPLICATIONS
Dead loads
Live loads
axial (tension- compression) ,
flexural (bending)
torsion(twisting) in nature.
Steady loads
Variable loads
Shock loads (suddenly)
Impact loads (applied with some velocity)
Thermal Loading

3. Static Load Stress Stress Ratio, R = 1.0
F and P are applied and remain constant
Stress
A static (steady) load is a stationary force or couple (applied to a member) that does not change in magnitude, point of application, and direction.
Stress Ratio, R = 1.0
Time

4. Dynamic Load: An element subjected to Dynamic loads
(tensile and compressive stresses involved)
Continuous total load reversal over time

5. Dynamic Load….
Loads that vary during normal service of the product …..& produce dynamic stresses
Dynamic stress can be cyclic or random.
Parts subject to dynamic stress?

6. a) & b) Schematic diagram of Gear train system
c) & d) Schematic diagram of Cone pulley drive
for propeller fan

7. The design involves Deflection and Rigidity Stress and Strength
(a) Bending deflection
(b) Torsional deflection
(c) Shear deflection due to transverse loading
Stress and Strength
(a) Static Strength
(b) Fatigue Strength
(c) Impact Strength
Product Reliability

8. Failure Examples
Fig. 5–1
Failure of truck driveshaft spline due to corrosion fatigue
Shigley’s Mechanical Engineering Design

9. Failure Examples Impact failure of a lawn-mower blade driver hub.
Fig. 5–2
Impact failure of a lawn-mower blade driver hub.
The blade impacted a surveying pipe marker.
Shigley’s Mechanical Engineering Design

10. Failure Examples
Fig. 5–3
Failure of an overhead-pulley retaining bolt on a weightlifting machine.
A manufacturing error caused a gap that forced the bolt to take the entire moment load.
Shigley’s Mechanical Engineering Design

11. Failure Examples
Fig. 5–5
Valve-spring failure caused by spring surge in an oversped engine.
The fractures exhibit the classic 45 degree shear failure
Shigley’s Mechanical Engineering Design

12. Strength Vs Stress Stress is dependent on the load characteristics.
Strength is an inherent property of the material. .
Factor of safety = Strength / Stress = S / σ
Factor of safety depends on
Type of material
How controllable are environment conditions
Type of loading and the degree of certainty
with which the stresses are calculated
Type of application
Failure can mean a part
has separated into two or more pieces; (brittle)
has become permanently distorted, thus ruining its geometry; (ductile)
has had its function compromised

13. Allowable stress
. . . While designing a component, it must be ensured that the maximum stress that may be induced during working life, do not exceed a certain safe limit . .
Such a safe limiting stress is known as allowable, permissible or design stress

14. Tensile Strength : Comparison
Si crystal
<100>
Graphite/
Ceramics/
Semicond
Metals/
Alloys
Composites/
fibers
Polymers
Tensile
strength, TS
(MPa)
PVC
Nylon 6,6 10
100
200
300
1000 Al
(6061) a ag Cu
(71500) hr Ta
(pure) Ti
Steel
(1020)
(4140) qt
(5Al-2.5Sn) W cw L
DPE PP PC
PET 20 30 40
2000
3000
5000
Graphite
Al oxide
Concrete
Diamond
Glass-soda
Si nitride H
wood
( fiber)
wood(|| fiber) 1
GFRE
(|| fiber)
( fiber) C
FRE A
FRE( fiber)
E-glass fib
Aramid
fib
Room Temp. values
Based on data in Table B4,
Callister 7e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered
AFRE, GFRE, & CFRE =
aramid, glass, & carbon
fiber-reinforced epoxy
composites, with 60 vol%
fibers.

16. Mechanical Properties
Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal

18. TENSILE STRESS: When a body is subjected to two equal and
opposite axial pulling forces, F - F as shown in
Fig.
the stress induced at any section A – A of the body is known as tensile stress and the corresponding strain, the tensile strain (the ratio of total elongation, 8 to the original length, l).

19. COMPRESSIVE STRESS:
When a body is subjected to two equal and opposite axial pushing forces, F

25. SHEAR STRESS:
Single shearing of a riveted joint.
When a body is subjected to two equal and opposite forces acting tangentially across the resisting section, as a result of which the body tends to shear off the section, then the stress induced is called shear stress.

26. the area resisting the shear off the rivet
Double shearing of a riveted joint.

29. Bearing Stress A localised compressive stress at the surface of
contact between two members of a machine part,
that are relatively at rest is known as bearing stress or crushing stress.
the bearing stress or crushing stress (stress at the surface of contact
between the rivet and a plate

31. Torsional Shear Stress
When a machine member is subjected to the action of two equal and opposite couples acting in parallel planes (or torque or twisting moment), then the machine member is said to be subjected to torsion.

33. Consider a straight beam subjected to a bending moment M
as shown in Fig.
The bending equation
is given by

36. Load and stress analysis:
A footstep to design Static strength

38. Load and stress analysis:
A footstep to design Static strength
PRINCIPAL STRESSES / PLANES Analytical approach

39. plane-stress transformation equations
2D –General Stress State
plane-stress transformation equations

40. 1 2 Equation (1) defines two particular values for the angle 2φp,
the maximum normal stress σ1
and the other,
the minimum normal stress σ2.
These two stresses are called the principal stresses,
The angle between the principal directions is 90°. 2
Equation (2) defines the two values of 2φs at which the shear stress τ reaches an extreme value.
The angle between the surfaces containing the maximum shear stresses
is 90°

41. Determination of principal and shear stresses
Formulas for the two principal stresses can be obtained by
The two extreme-value of
shear stresses are found to be

42. Using Mohr’s circle, finding the principal stresses and directions: graphical approach

44. Failure Theories – Static Loads